Predicting Nonlinear Chaotic Systems with Incomplete Information via the Dynamical System Deep Learning Method

Predicting Nonlinear Chaotic Systems with Incomplete Information via the Dynamical System Deep Learning Method | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Predicting Nonlinear Chaotic Systems with Incomplete Information via the Dynamical System Deep Learning Method Hao Li, Jianping Li, Zixiang Wu, Mingyu Wang, Guangcan Liu, Ning Wang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9210324/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Predicting the evolution of nonlinear chaotic dynamical systems is vital across numerous scientific disciplines. However, real-world applications are often hindered by incomplete observational data, characterized by either missing state variables or temporal gaps, posing challenges for traditional data-driven methods that rely heavily on complete inputs or data imputation. The recently proposed Dynamical System Deep Learning (DSDL) method, grounded in Takens’ delay embedding theorem, possesses the capability to infer global system dynamics from partial observations. In this study, we define various scenarios of incomplete information, evaluate the predictive performance of DSDL in two typical scenarios, and compare it with mainstream deep learning methods such as ANN, RC-ESN, LSTM, NG-RC, and SINDy. The results demonstrate that the DSDL method achieves the optimal predictive performance across all scenarios and exhibits the highest stability over multiple trials, indicating its capability to infer global system dynamics from partial information. This method provides a novel perspective for addressing prediction challenges under incomplete information conditions, thereby enriching the research on predicting complex nonlinear dynamical systems. Furthermore, it offers technical support for predicting real-world infinite-dimensional nonlinear chaotic dynamical systems, such as the atmosphere and oceans. nonlinear chaotic dynamical systems dynamical system deep learning incomplete information deep learning methods Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 12 May, 2026 Reviews received at journal 21 Apr, 2026 Reviewers agreed at journal 21 Apr, 2026 Reviewers agreed at journal 21 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviewers invited by journal 20 Apr, 2026 Editor assigned by journal 25 Mar, 2026 Submission checks completed at journal 25 Mar, 2026 First submitted to journal 24 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9210324","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627551142,"identity":"7cc0f4b9-e6ed-4f30-b679-4e61fdd63f30","order_by":0,"name":"Hao Li","email":"","orcid":"","institution":"Ocean University of China","correspondingAuthor":false,"prefix":"","firstName":"Hao","middleName":"","lastName":"Li","suffix":""},{"id":627551143,"identity":"d7470ef7-a8cd-4858-858c-548e22a49f4c","order_by":1,"name":"Jianping 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